PolynomialRegression/Polynomial Regression.ipynb
Anna Nowak 33c8095ad0 ploty
2021-06-28 11:21:19 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Algorytm najszybszego spadku dla regresji wielomianowej. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Skład grupy:\n",
"- Nowak Anna,\n",
"- Łaźna Patrycja,\n",
"- Bregier Damian"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 0. Podstawowe informacje o zbiorze danych"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"Ze względu na specyfikę wytycznych projektu zakładającego wykorzystanie jedynie dwóch cech: x i y oraz modelowanie zależności y od x za pomocą funkcji wielomianowej dobrany został przez nas odpowiedni dataset. Obejmuje on jedynie trzy kolumny, czyli: płeć, wzrost w calach oraz wagę w funtach, z czego ze względu na specyfikę projektu wykorzystywane są jedynie wzrost oraz waga. Każdy z parametrów zawiera po 10 tysięcy unikalnych wartości.\n",
"\n",
"![image.png](attachment:image.png)\n",
"\n",
"Dokładne informacje na temat tego zbioru, jego zawartości i samych danych można znaleźć pod adresem: https://www.kaggle.com/mustafaali96/weight-height."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import random\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import ipywidgets as widgets\n",
"np.set_printoptions(suppress=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Wczytywanie i preprocessing danych"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Stopień wielomianu\n",
"degree = 4\n",
"plot_degree = 1\n",
"X_plot = np.linspace(0, 100, 1000)\n",
"initial_theta = np.matrix([0] * (degree + 1)).reshape(degree + 1, 1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Wybór dwóch kolumn - dotyczących wzrostu i wagi\n",
"data = pd.read_csv('weight-height.csv')[[\"Height\", \"Weight\"]]\n",
"# Czyszczenie tabeli i wartości pustych\n",
"data = data.dropna()\n",
"data_matrix = np.matrix(data)\n",
"\n",
"m, n_plus_1 = data_matrix.shape\n",
"n = n_plus_1 - 1\n",
"X = (np.ones((m, 1)))\n",
"\n",
"for i in range(1, degree + 1):\n",
" Xn = np.power(data_matrix[:, 0:n], i)\n",
" Xn /= np.amax(Xn, axis=0)\n",
" X = np.concatenate((X, Xn), axis=1)\n",
"\n",
"X = np.matrix(X).reshape(m, degree * n + 1)\n",
"Y = np.matrix(data_matrix[:, -1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Metody regresji wielomianowej"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"Regresja wielomianowa służy do obliczania zależności pomiędzy zmienną zależną a jedną lub więcej zmiennymi niezależnymi, które mogą występować w wyższych potęgach. Wykorzystywana w przypadku zbiorów cechujacych się nieliniowymi zależnościami.\n",
"\n",
"Równanie regresji wielomianowej:\n",
"![image.png](attachment:image.png)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def print_theta(theta):\n",
" print(\"f(x) = \", end=\"\")\n",
" for i,x in enumerate(theta.tolist()[:-1]):\n",
" x = x[0]\n",
" print(f\"{x}x^{i}\", end=\" + \")\n",
" print(f\"{theta.tolist()[-1][0]}^{len(theta) - 1}\")\n",
"\n",
"# Implementacja wzoru na regresję wielomianową\n",
"def polynomial_regression(theta, x):\n",
" x = x/data[\"Height\"].max()\n",
" return sum(theta * np.power(x, i) for i, theta in enumerate(theta.tolist()))\n",
"\n",
"# Implementacja wzoru na RMSE, czyli pierwiastek z błędu średniokwadratowego\n",
"def mean_squared_error(theta, X, Y):\n",
" J = 1.0 / (2.0 * m) * ((X * theta - Y).T * (X * theta - Y))\n",
" return J.item()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Wybrane rodzaje gradientów"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"Metoda gradientu prostego to algorytm numeryczny mający na celu znalezienie minimum lokalnego dla zadanej funkcji celu. Jak sama nazwa wskazuje jest to jedna z prostszych metod, która opiera się na iteracyjnym poszukiwaniu minimum. Proces ten (dla pierwszych czterech kroków), został pokazany na poniższym rysunku.\n",
"![image.png](attachment:image.png)"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"Metoda gradientu prostego\n",
"![image.png](attachment:image.png)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# Wzór na gradient prosty\n",
"def gradient(theta, X, Y):\n",
" return 1.0 / len(Y) * (X.T * (X * theta - Y)) "
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"Metoda najszybszego spadku jest iteracyjnym algorytmem wyszukiwania minimym zadanej funkcji celu i stanowi modyfikację gradientu prostego. Na samym początku algorytmu wybierany jest punkt startowy, w którym jest obliczany antygradient funkcji celu stanowiący kierunek poszukiwań w procedurze. Kolejny krok jest obliczany w oparciu o poprzedni i jeżeli nie spełnia on warunku stopu to obliczenia są powtarzane do skutku. \n",
"\n",
"Podstawową różnicę w stosunku do gradientu prostego stanowi sposób wyszukiwania wartości, która jest dokonywana przez minimalizację kierunkową funkcji. \n",
"\n",
"![image.png](attachment:image.png)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# Steepest descent\n",
"def steepest_descent(X, Y, theta, cost_function = mean_squared_error, \n",
" single_step=0.01, epochs=30):\n",
" cost = cost_function(theta, X, Y)\n",
" logs = [[cost, theta]]\n",
" for i in range(epochs):\n",
" direction = gradient(theta, X, Y)\n",
" j = 0\n",
" while(True):\n",
" j+=1\n",
" next_theta = theta - single_step * direction\n",
" next_cost = cost_function(next_theta, X, Y)\n",
" if(next_cost >= cost or type(next_cost) != float):\n",
" break\n",
" cost = next_cost\n",
" theta = next_theta\n",
" logs.append([next_cost, theta])\n",
" return theta, logs"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ponadto w toku prac projektowych przetestowane zostaly także inne algorytmy takie jak batch gradient descend (BGD), BGD z momentum, mini-batch gradient descend oraz stochastic gradient descend. \n",
"\n",
"BGD to metoda w której błąd obliczany jest dla każdego parametru ze zbioru treningowego, ale sam model jest aktualizowany dopiero po ocenie wszystkich danych. \n",
"\n",
"MBGD opiera się na podziale danch treningowych na niewielkie pakiety, które są potem wykorzystywane do obliczania wartości błędu i aktualizacji modelu.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"# Batch gradient descend (BGD)\n",
"def BGD(X, Y, theta, cost_function = mean_squared_error, learning_rate=0.1, \n",
" eps=10**-5, max_steps = 10000000000):\n",
" cost = cost_function(theta, X, Y)\n",
" logs = [[cost, theta]]\n",
" \n",
" for i in range(max_steps):\n",
" theta = theta - learning_rate * gradient(theta, X, Y)\n",
" next_cost = cost_function(theta, X, Y)\n",
" logs.append([next_cost, theta])\n",
" if abs(cost - next_cost) <= eps:\n",
" break\n",
" cost = next_cost\n",
" return theta, logs\n",
"\n",
"# BGD z momentum\n",
"def momentum(X, Y, theta, cost_function = mean_squared_error, \n",
" learning_rate=0.1, momentum = 0.3, epochs=30, degree=degree):\n",
" cost = cost_function(theta, X, Y)\n",
" logs = [[cost, theta]]\n",
" delta_history = [np.matrix([0]*(degree+1)).T]\n",
" for i in range(epochs):\n",
" delta_history.append(momentum * delta_history[-1] + \n",
" learning_rate * gradient(theta, X, Y))\n",
" theta = theta - delta_history[-1]\n",
" next_cost = cost_function(theta, X, Y)\n",
" logs.append([next_cost, theta])\n",
" cost = next_cost\n",
" return theta, logs\n",
"\n",
"# Mini-batch gradient descend (MBGD)\n",
"def MBGD(X, Y, theta, cost_function = mean_squared_error, \n",
" learning_rate=0.1, epochs=5, batch_size=16):\n",
" cost = cost_function(theta, X, Y)\n",
" logs = [[cost, theta]]\n",
" start, end = 0, batch_size\n",
" \n",
" steps = m / batch_size\n",
" for i in range(epochs):\n",
" zipped_XY = list(zip(X, Y))\n",
" random.shuffle(zipped_XY)\n",
" X_shuffled, Y_shuffled = zip(*zipped_XY)\n",
" X_shuffled = np.concatenate(X_shuffled, axis=0) \n",
" Y_shuffled = np.concatenate(Y_shuffled, axis=0) \n",
" for j in range(int(steps)):\n",
" batch = X_shuffled[start:end,:], Y_shuffled[start:end,:]\n",
" theta = theta - learning_rate * gradient(theta, batch[0], batch[1])\n",
" cost = cost_function(theta, X, Y)\n",
" logs.append([cost, theta])\n",
"\n",
" if start + batch_size < batch_size:\n",
" start += batch_size\n",
" else:\n",
" start = 0\n",
" end = min(start + batch_size, m)\n",
" return theta, logs\n",
"\n",
"# Stochastic gradient descend (SGD)\n",
"def SGD(X, Y, theta, cost_function = mean_squared_error, learning_rate=0.1,\n",
" epochs=5):\n",
" return MBGD(X, Y, theta, cost_function, learning_rate, epochs, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Zestawienie wyników"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"final_theta_SGD, logs_3 = SGD(X, Y, initial_theta, epochs = 60)\n",
"print(\"SGD:\")\n",
"print_theta(final_theta_SGD)\n",
"print(f\"{len(logs_3)} updates\\n\")\n",
"\n",
"final_theta_BGD, logs_1 = BGD(X, Y, initial_theta)\n",
"print(\"BGD:\")\n",
"print_theta(final_theta_BGD)\n",
"print(f\"{len(logs_1)} updates\\n\")\n",
"\n",
"final_theta_MBGD, logs_2 = MBGD(X, Y, initial_theta, epochs = 60)\n",
"print(\"MBGD:\")\n",
"print_theta(final_theta_MBGD)\n",
"print(f\"{len(logs_2)} updates\\n\")\n",
"\n",
"\n",
"final_theta_momentum, logs_4 = momentum(X, Y, initial_theta, epochs = 60)\n",
"print(\"momentum:\")\n",
"print_theta(final_theta_momentum)\n",
"print(f\"{len(logs_4)} updates\\n\")\n",
"\n",
"final_steepest_descent, logs_5 = steepest_descent(X, Y, initial_theta, epochs = 60)\n",
"print(\"steepest descent:\")\n",
"print_theta(final_steepest_descent)\n",
"print(f\"{len(logs_5)} updates\\n\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wniosek:\n",
"Metoda najszybszego spadku oraz momentum cechują się najszybszą zbieżnością do minimum lokalnego danej funkcji. Przeciętnie, dla zadanych parametrów, minimum jest osiągane w ciągu 61 aktualizacji. Podczas gdy SGD wymaga ich ponad 600 tysięcy. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5. Reprezentacja graficzna regresji wielomianowej i funkcji kosztu"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"def plot_polynomial_regression(theta):\n",
" fig = plt.figure(figsize=(10,5))\n",
" Y_plot = polynomial_regression(theta, X_plot).tolist()\n",
" chart = fig.add_subplot()\n",
" chart.plot(data[\"Height\"], Y ,\"go\")\n",
" chart.plot(X_plot, Y_plot, color=\"red\", lw=2, label=f\"degree {len(theta)}\")\n",
" plt.ylim([0,250])\n",
" plt.show()\n",
" \n",
"\n",
"def plot_cost_function(logs):\n",
" no_iter = no_iter = [x for x in range(1, len(logs) + 1)]\n",
" all_cost = [row[0] for row in logs]\n",
" \n",
" fig = plt.figure(figsize=(10,5)) \n",
" plt.plot(no_iter, all_cost)\n",
" plt.xlabel('No. of iterations')\n",
" plt.ylabel('Cost')\n",
" plt.show()\n",
" \n",
"\n",
"print(\"BGD:\")\n",
"plot_polynomial_regression(final_theta_BGD)\n",
"plot_cost_function(logs_1)\n",
"print(\"MBGD:\")\n",
"plot_polynomial_regression(final_theta_MBGD)\n",
"plot_cost_function(logs_2)\n",
"print(\"SGD:\")\n",
"plot_polynomial_regression(final_theta_SGD)\n",
"plot_cost_function(logs_3)\n",
"print(\"Momentum:\")\n",
"plot_polynomial_regression(final_theta_momentum)\n",
"plot_cost_function(logs_4)\n",
"print(\"Metoda najszybszego spadku:\")\n",
"plot_polynomial_regression(final_steepest_descent)\n",
"plot_cost_function(logs_5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Wizualizacja metody najszybszego spadku dla wielomianu drugiego stopnia"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"initial_theta_plot = np.matrix([0] * (plot_degree + 1)).reshape(plot_degree + 1, 1)\n",
"m, n_plus_1 = data_matrix.shape\n",
"n = n_plus_1 - 1\n",
"X_plot = (np.ones((m, 1)))\n",
"\n",
"for i in range(1, plot_degree + 1):\n",
" Xn = np.power(data_matrix[:, 0:n], i)\n",
" Xn /= np.amax(Xn, axis=0)\n",
" X_plot = np.concatenate((X_plot, Xn), axis=1)\n",
"\n",
"X_plot = np.matrix(X_plot).reshape(m, plot_degree * n + 1)\n",
"Y_plot = np.matrix(data_matrix[:, -1])\n",
"\n",
"\n",
"steepest_descent_deg_2, logs_deg_2 = steepest_descent(X_plot, Y_plot, initial_theta_plot, epochs = 60)\n",
"momentum_deg_2, logs_momentum_2 = momentum(X_plot, Y_plot, initial_theta_plot, epochs = 60, degree=1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cost_history = [row[0] for row in logs_deg_2]\n",
"all_thetas = [row[1] for row in logs_deg_2]\n",
"\n",
"\n",
"theta0_history = [row[0].item() for row in all_thetas]\n",
"theta1_history = [row[1].item() for row in all_thetas]\n",
"\n",
"cost_history = np.array(cost_history)\n",
"theta0_history = np.array(theta0_history)\n",
"theta1_history = np.array(theta1_history)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cost_history_momentum = [row[0] for row in logs_momentum_2]\n",
"all_thetas_momentum = [row[1] for row in logs_momentum_2]\n",
"\n",
"theta0_history_momentum = [row[0].item() for row in all_thetas_momentum]\n",
"theta1_history_momentum = [row[1].item() for row in all_thetas_momentum]\n",
"\n",
"cost_history_momentum = np.array(cost_history_momentum)\n",
"theta0_history_momentum = np.array(theta0_history_momentum)\n",
"theta1_history_momentum = np.array(theta1_history_momentum)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"theta0_vals = theta0_history\n",
"theta1_vals = theta1_history\n",
"J_vals = np.zeros((len(theta0_vals), len(theta1_vals)))\n",
"\n",
"c1=0\n",
"c2=0\n",
"pom = 0\n",
"for i in theta0_vals:\n",
" for j in theta1_vals:\n",
" t = np.array([i, j])\n",
" J_vals[c1][c2] = cost_history[pom]\n",
" c2=c2+1\n",
" c1=c1+1\n",
" pom += 1\n",
" c2=0"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"theta0_vals_momentum = theta0_history_momentum\n",
"theta1_vals_momentum = theta1_history_momentum\n",
"J_vals = np.zeros((len(theta0_vals_momentum), len(theta1_vals_momentum)))\n",
"\n",
"c1=0\n",
"c2=0\n",
"pom = 0\n",
"for i in theta0_vals_momentum:\n",
" for j in theta1_vals_momentum:\n",
" t = np.array([i, j])\n",
" J_vals[c1][c2] = cost_history_momentum[pom]\n",
" c2=c2+1\n",
" c1=c1+1\n",
" pom += 1\n",
" c2=0"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import plotly.express as px\n",
"fig = px.line_3d(x=theta0_vals, y=theta1_vals, z=[x[0] for x in J_vals])\n",
"fig.show()\n",
"fig2 = px.line_3d(x=theta0_vals_momentum, y=theta1_vals_momentum, z=[x[0] for x in J_vals])\n",
"fig2.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import plotly.graph_objects as go\n",
"\n",
"fig = go.Figure(data=[go.Surface(x=theta0_vals, y=theta1_vals, z=J_vals)])\n",
"fig.update_layout(title='Loss function for different thetas', autosize=True,\n",
" width=600, height=600, xaxis_title='theta0', \n",
" yaxis_title='theta1')\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import plotly.graph_objects as go\n",
"\n",
"fig = go.Figure(data=[go.Surface(x=theta0_vals_momentum, y=theta1_vals_momentum, z=J_vals)])\n",
"fig.update_layout(title='Loss function for different thetas', autosize=True,\n",
" width=600, height=600, xaxis_title='theta0', \n",
" yaxis_title='theta1')\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 6. Regresja wielomianowa z wykorzystaniem gotowych bibliotek"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
"from sklearn.pipeline import make_pipeline\n",
"from sklearn.linear_model import Ridge, LinearRegression"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"model = make_pipeline(PolynomialFeatures(degree=degree, include_bias=True), \n",
" LinearRegression())\n",
"model.fit(data[[\"Height\"]],Y)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Y_plot_2 = model.predict([[x] for x in X_plot])\n",
"\n",
"fig = plt.figure(figsize=(10,5))\n",
"chart = fig.add_subplot()\n",
"chart.plot(data[\"Height\"], Y ,\"go\")\n",
"chart.plot(X_plot, Y_plot_2, color=`\"red\", lw=2, label=f\"degree {degree}\")\n",
"plt.ylim([0,250])\n",
"plt.xlim([0,100])\n",
"degree"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"polyfit_theta = np.polyfit(data[\"Height\"]/data[\"Height\"].max(), Y, degree)\n",
"plot_polynomial_regression(polyfit_theta)"
]
}
],
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